Block #93,684

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/2/2013, 2:40:22 PM · Difficulty 9.1954 · 6,696,256 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

d8da576535e6ec025f43b58861bb708ccdcb74c8bea7e798d49877706fa5c099

View on Chainz ↗

Height

#93,684

Difficulty

9.195419

Transactions

Size

203 B

Version

Bits

09320703

Nonce

67,603

Timestamp

8/2/2013, 2:40:22 PM

Confirmations

6,696,256

Merkle Root

0dbae35e209a87a11895c8559063be9b985d2600f711ba73da88eadeb90217e1

Transactions (1)

Coinbase0dbae35e209a87…88eadeb90217e1

1 in → 1 out11.8100 XPM109 B

AK1JUKWL…oPR4rN5o

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.574 × 10¹⁰⁴(105-digit number)

25747690278017094093…63804359282566529419

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.574 × 10¹⁰⁴(105-digit number)

25747690278017094093…63804359282566529419

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.574 × 10¹⁰⁴(105-digit number)

25747690278017094093…63804359282566529421

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

5.149 × 10¹⁰⁴(105-digit number)

51495380556034188186…27608718565133058839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.149 × 10¹⁰⁴(105-digit number)

51495380556034188186…27608718565133058841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.029 × 10¹⁰⁵(106-digit number)

10299076111206837637…55217437130266117679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.029 × 10¹⁰⁵(106-digit number)

10299076111206837637…55217437130266117681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.059 × 10¹⁰⁵(106-digit number)

20598152222413675274…10434874260532235359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.059 × 10¹⁰⁵(106-digit number)

20598152222413675274…10434874260532235361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

4.119 × 10¹⁰⁵(106-digit number)

41196304444827350549…20869748521064470719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer